Select the correct answer.
Tracy wants to make a cylindrical model. The height of the cylindrical model, H(V), in inches, is modeled by this
equation, where Vis the volume of the cylindrical model, in cubic inches.
H(V) = 2. 6937
What is the average rate of change of the model's height when its volume changes from 512 cubic inches to
1,000 cubic inches?
The model's height increases by approximately 21. 52 inches for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 022 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 011 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 26. 9 inches for every 1-cubic-inch increase in its volume.
Answers
The average rate of change of the height function is slope of the height function
The model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
How to determine the average rate of change?The height function is given as:
[tex]H(V) = 2.69\sqrt[3]{V}[/tex]
When V = 512, the function becomes
[tex]H(512) = 2.69\sqrt[3]{512}[/tex]
[tex]H(512) = 21.52[/tex]
Similarly;
When V = 1000, the function becomes
[tex]H(1000) = 2.69\sqrt[3]{1000}[/tex]
[tex]H(1000) = 26.9[/tex]
The average rate of change is then calculated as:
[tex]H' = \frac{H(1000) - H(512)}{1000 - 512}[/tex]
This gives
[tex]H' = \frac{26.9 - 21.52}{1000 - 512}[/tex]
[tex]H' = \frac{5.38}{488}[/tex]
Evaluate the quotient
[tex]H' = 0.01102459016[/tex]
Approximate
[tex]H' = 0.011[/tex]
Hence, the model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
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Answer:
The model’s height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
Step-by-step explanation:
Plato/Edmentum
Related Questions
just trying some stuff coz i dont use this ttoo much
Answers
Step-by-step explanation:
ohhhhhhhhhhhhhhhh.......
Harry is trying to solve the equation 0 = 2x2 − x − 6 using the quadratic formula. He has made an error in one of the steps below. Find the step where Harry went wrong. (1 point)
Answers
➙ a quadratic equation in which Harry lagged due to an error made by him, 2x² - x - 6= 0
To solve -➙ the given quadratic equation.
Concept applied -➙ We will apply the quadratic formula as given in the question. So, let's study about quadratic equation first because we are supposed to apply the formula in equation.
What is quadratic equation?
➙ A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0.
Now, what is quadratic formula?
➙The roots of a quadratic equation ax + bx + c = 0 are given by [tex]\sf{\:\frac{-b \pm\: \sqrt {b ^ 2 - 4ac}}{2a}}[/tex] provided b - 4ac ≥ 0.
Solution -here as per the given quadratic equation,
a = 2, b = -1 and c = -6
putting in the formula,
[tex]\implies\sf{x=\frac{-(-1) \pm\: \sqrt {(-1)^2 - 4(2)(-6)}}{2(2)}}[/tex]
[tex]\implies\sf{x=\frac{1 \pm\: \sqrt {1+48}}{4}}[/tex]
[tex]\implies\sf{x=\frac{1 \pm\: \sqrt {49}}{4}}[/tex]
[tex]\implies\sf{x=\frac{1 \pm\: 7}{4}}[/tex]
Solving one by one,
[tex]\implies\sf{x=\frac{1 + \: 7}{4}}[/tex]
[tex]\implies\sf{x=\frac{8}{4}}[/tex]
[tex]\implies{\boxed{\bf{x=2}}}[/tex]
________________
[tex]\implies\sf{x=\frac{1 - \: 7}{4}}[/tex]
[tex]\implies\sf{x=\frac{-6}{4}}[/tex]
[tex]\implies{\boxed{\bf{x=\frac{-3}{2}}}}[/tex]
________________________________
Note - Hey dear user!! You haven't provided the solution which was solved by Harry (A.T.Q). Please go through the solution as it will help you to find the error done by Harry.
________________________________
Hope it helps!! (:
can someone explain what to do like im a 5 year old please? (pre algebra)
Answers
Answer:
angle 3 = 61
angle 4 = 119
angle 6 = 61
angle 7 = 119
Step-by-step explanation:
there are a few ways you could look at this
first, each angle that is diagonal from eachother is going to be equal so 1 is the same as 3, 2 is the same as 4 etc
also each line going across has to be 180° so if angel 1 was 175 then angle 2 has to be 5 so when you combine them it becomes 180
if you look at the sizes some are bigger than the others, because you're given angle 1 = 61 then all the other small angles would be 61 too, and 180 - 61 = 119 so the all the big ones have to be 119
if this confused u more I'm sorry lol let me know if this helped
What is the perimeter of this garden?
A:94 ft
B 100ft
C 76ft
D 600ft
Answers
Answer:
A
Step-by-step explanation:
Hope this helped
HELP!!!! I can’t figure this out
Answers
Answer:
[tex]A.\,\orange{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]
Step-by-step explanation:
[tex] \frac{x + 2}{ {x}^{2} + 5x + 6 } \div \frac{3x + 1}{ {x}^{2} - 9} \\ \\ = \frac{x + 2}{ {x}^{2} + 3x + 2x+ 6 } \div \frac{3x + 1}{ {x}^{2} - {(3)}^{2} } \\ \\ = \frac{\cancel{x + 2}}{ \cancel{{({x}+ 3)}} \cancel{(x+ 2) }} \times \frac{\cancel{( {x} + 3)}( {x} - {3)}}{3x + 1} \\ \\ = \purple{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]
The tree diagram below shows all of the possible outcomes for flipping three coins.
A tree diagram has outcomes (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T).
What is the probability that at least two of the coins will be tails?
Answers
Answer:
1/2
Step-by-step explanation:
Let H = the possible outcomes that include flipping heads
Let T = the possible outcomes that include flipping tails
In order to have an outcome of two coins having tails, that means for each outcome, you must have at least two T's.
Therefore, the possible outcomes are:
(H, T, T)
(T, H, T)
(T, T, H)
(T, T, T)
This is 4 possible outcomes, and since we want to find the probability we find the total number of outcomes and make a fraction.
[tex]4/8 = 1/2[/tex]
There are 8 outcomes, and since 4 work for this scenario, the answer is 1/2.
#LearnWithBrainly
Is (1, 13) a solution to this system of equations?
y = 8x + 5
y = 13
Yes or No
Answers
Answer:
yes
Step-by-step explanation:
i hope this will help
у
6
2 Look at the coordinate plane at the right.
Choose True or False for each statement about the points in the
coordinate plane.
5
4
L
a.
3
Point J and point Khave the same
y-coordinate.
True
False
2.
1
K
b. Point K and point L have the same
x-coordinate.
True
False
O
► X
6
1
2
3
4
5
c. Point J and point L are the same
distance up from the origin.
True
False
True
False
d. The y-coordinate of point L is 5.
e.
Point is the nearest point to the
right of the origin.
True
False
Answers
Answer:
A. False
B. True
C. False
D. True
E. False
Suppose that $x,y,z$ are positive integers satisfying $x \le y \le z$, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of $z$
Answers
The possible values of z is an illustration of the sum operator
The sum of all possible values of z is 17
How to determine the possible sum of z?The conditions in the question are:
x <= y <= z
xyz = 2(x + y + z)
Using the trial by error method, the possible values of x, y and z are:
x = 1 , y = 3 , z = 8x = 1 , y = 4 , z = 5x = 2 , y = 2 , z = 4The sum of the z values are:
z = 8 + 5 + 4
Evaluate the sum
z = 17
Hence, the sum of all possible values of z is 17
Read more about the sum operator at:
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A farmer has a total of 23 pigs and chickens. The 23 animals have a total
of 60 legs. How many pigs and how many chickens does the farmer have?
Answers
Answer:
7 pigs, 16 chickens
Step-by-step explanation:
p= pigs, c= chickens, legs= 60, number of pigs & chickens= 23
System of Equations:
Equation 1: [tex]p+c=23[/tex] would be [tex]23-p=c[/tex]Equation 2: [tex]4p+2c=60[/tex] for the legsThen, use substitution & solve:
[tex]4p+2(23-p)=54\\4p+46-2p=54\\4p-2p=8\\2p=8\\p=7[/tex]Now, plug [tex]p=7[/tex] back into [tex]23-p=c[/tex] to get c
[tex]23-p=c\\23-7=c\\c=16[/tex]Answer: 7 pigs, 16 chickens or [tex]p=7[/tex] and [tex]c=16[/tex]
To check your work, plug those solutions back into the system.------
(I hope that helps & good luck! <3)
how do i find slope in standard form?
Answers
Answer:
The standard form of a linear equation is Ax + By = C. When we want to find the slope of the line represented by this equation, we have two options. We can put the equation in slope-intercept form and identify the slope that way, or we can use the formula m = -A/B.
Answer:
m = -A/B
The standard form of a linear equation is Ax + By = C.
[tex]hope \: it \: will \: help \: [/tex]
i will mark brainliest rn
Answers
Answer:
65 is the correct answer
Please just help. I’m stuck on math! Determining spinner probability Lol BUT please help! If you know how to do this
Answers
1. 2
2. 2
3. 4
4. 3 and 1
5. C
6. B
7. C and D
8. 3
9. 1 and 4
10. C
11. 2
12. D
You're Welcome✌! Brainliest would mean a lot.
solve for x and please roundddd
Answers
We know the lengths of the adjacent and opposite sides when looking at the angle x, so we use those two sides to find the trig ratio.
So we use Opposite/adjacent (Tangent) Which is 54/72=0.75
Now we get out the trig ratio table. Because we used the tangent ratio (O/A) , we use that column to look for the closest number to 0.75.
The closest is 0.754, and the degree for it is 37 degrees
Rlly hope this helps :)))
Clinton has a spinner labeled orange, blue, green and pink. He spins the spinner 100 times. He gets orange 33 times. What the experimental probability of him getting an orange? in fraction form
Answers
Explanation:
Divide the number of times orange shows up (33) over the number of total spins (100). Reduce the fraction if possible. In this case, 33/100 is fully reduced because 33 and 100 have no common factors other than 1.
Help on this please.
Answers
Answer: 33.88 meters
Step-by-step explanation:
Justin buys candy that costs $6 per pound. he will buy at most 9 pounds of candy. what are the possible amounts he will spend on candy? use for the amount (in dollars) justin will spend on candy. write your answer as an inequality solved for c.
Answers
Using proportions, it is found that the possible amounts that he will spend on candy are represented by the inequality [tex]c \leq 54[/tex].
What is a proportion?A proportion is a fraction of a total amount.
In this problem, each pound of candy costs $6, and he will buy at most 9 pounds, hence the maximum amount he will spend is given by:
M = $6 x 9 = $54.
Hence, the possible amounts that he will spend on candy are represented by the inequality [tex]c \leq 54[/tex].
More can be learned about proportions at https://brainly.com/profile/joaobezerra-15918078
The interior angle of a regular polygon is 154°, What is
the size of an exterior angle?
Answers
Answer: 26 degrees
Step-by-step explanation:
An interior angle and its exterior angle are supplementary.
(from Unit 5, Lesson 7) Below is a set of data about temperatures. The range of a set of data is the distance between the lowest and highest value in the set. What is the range of these temperatures? 9°C, -3°C, 22°C, -5°C, 11°C, 15°C Type your answer in the box below. The range of temperatures is .
Answers
27ﾟC
Given the temperatures, 9ﾟC, -3ﾟC, 22ﾟC, -5ﾟC, 11ﾟC, 15ﾟC, the range difference between the highest temperature and lowest temperature is 27ﾟC.
22ﾟC - (-5ﾟC) = 27ﾟC
Write a formula that shows the dependence of: the length of the side (a) of a cube on the surface area (S) of the cube
Write the formula for the parabola that has x-intercepts (-3-√2,0) and (-3+√2,0), and y-intercept (0,-5)
Answers
Answer:
Let a = side length of a cube
Let S = surface area of a cube
Area of a square = a²
Since a cube has 6 square sides: S = 6a²
To make a the subject:
S = 6a²
Divide both sides by 6:
[tex]\sf \implies \dfrac{S}{6}=a^2[/tex]
Square root both sides:
[tex]\sf \implies a=\sqrt{\dfrac{S}{6}}[/tex]
(positive square root only as distance is positive)
-----------------------------------------------------------------------------------------------
[tex]\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0[/tex]
[tex]\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0[/tex]
Therefore,
[tex]\sf y=a(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex] for some constant a
Given the y-intercept is at (0, -5)
[tex]\sf \implies a(0+3+\sqrt{2}) (0+3-\sqrt{2})=-5[/tex]
[tex]\sf \implies a(3+\sqrt{2}) (3-\sqrt{2})=-5[/tex]
[tex]\sf \implies a(9-2)=-5[/tex]
[tex]\sf \implies 7a=-5[/tex]
[tex]\sf \implies a=-\dfrac57[/tex]
Substituting found value of a into the equation and simplifying:
[tex]\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]
[tex]\sf \implies y=-\dfrac57(x^2+6x+7)[/tex]
[tex]\sf \implies y=-\dfrac57x^2-\dfrac{30}{7}x-5[/tex]
The base of a triangle is 75 cm and its height is 12
12 cm. Find its area.
Answers
Answer:
Here is your answer
Step-by-step explanation:
Solution,
here,
Base is 75 cm
Height is 12 cm
Now,
Area of triangle=1/2×b×h
=1/2×75×12
= 900/2
=450. ans
PLEASE I NEED HELP!!! BRAINLIEST FOR THE FASTEST ANSWER
Answers
Answer:
883.125
Step-by-step explanation:
First, use the formula for volume of a sphere (4/3 * pi * r^3) to get the volume of the full sphere, then divide it by 2 to get the volume of half of the sphere.
Hopefully this helps- let me know if you have any questions!
Trigonometry, how would I find the area of this parallelogram?
Answers
Answer:
A ≈ 160 cm²
Step-by-step explanation:
the area (A) of a parallelogram given adjacent sides a and b and angle Θ between them is
A = absinΘ
here a = 12 , b = 15 and Θ = 117° , then
A = 12 × 15 × sin117° ≈ 160 cm²( to the nearest cm² )
in∆BDC
use sine rule for area
[tex]\\ \rm\rightarrowtail \dfrac{1}{2}absinC[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{1}{2}(12)(15)sin117[/tex]
[tex]\\ \rm\rightarrowtail 90(0.89)[/tex]
[tex]\\ \rm\rightarrowtail 80.1m^2[/tex]
Area of parallelogram=2(80.1)=160.2m^2The round temperature dial on a thermostat has a radius of 3 centimeters. What is the dial's diameter?
Answers
Answer:
6 cm
Step-by-step explanation:
A diameter of a circle is a line segment that connects one side of the circle to the other, passing through the center.
The distance from the center to any point on the circle is the radius. So, a diameter is the sum of a radius to one side of the circle and a radius to the other side of the circle. (The circle center is the midpoint of the diamter.)
The diameter is twice the radius:
d = 2 × (3 cm) = 6 cm
The dial's diameter is 6 cm.
Factor completely 4xy−24y−x+6
Answers
(4xy-24y)(-x+6)
4y(x-6) -1(x-6)
(4y-1)(x-6) is the factored form
rohana wants to find the volume of a sphere that has a radius of 10 feet. which equation can she use to solve for this value in cubic feet ?
Answers
The equation that can be used to determine the volume of the sphere is 4/3π10³
What is the volume of the sphere?A sphere is a three-dimensional object in which points from its center to its circumference is equidistant.
Volume of a sphere = 4/3πr³
Where:
π = pi = 22/7r = radiusTo learn more about the volume of a sphere, please check: https://brainly.com/question/13705125
karen and mary are saving money. karen has 150 and disposits an additional $25 a week. mary has $200 and deposits an additional $10 a week. what is the minimum number of weeks it will take for karen to have more saving then mary
Answers
Answer:
4 weeks
Step-by-step explanation:
original base amount 150 200
1st week deposit 175 210
2nd week deposit 200 220
3rd week deposit 225 230
4th week deposit 250 240
Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle could represent the base of the vase? Use 3. 14 for Pi.
Answers
The area of the vase lies between the area [tex]135\ cm^2[/tex] and [tex]155\ cm^2[/tex] will be [tex]153.86\ cm^2[/tex].
What will be the area?As we know that the area of the circle is given by the formula
[tex]A=\pi r^2[/tex]
So now from the question, we will find the radius for both the given areas.
Radius for the first area
[tex]r=\dfrac{A}{\pi} =\dfrac{135}{\pi} =6.56\ cm[/tex]
Radius for the second area
[tex]r=\dfrac{A}{\pi} =\dfrac{155}{\pi} =7.03\ cm[/tex]
Now we can see the range of the radius lies
[tex]6.56\leq r\leq 7.03[/tex]
The radius must be r=7 cm lie between two quantities.
Then the area at r= 7cm will be
[tex]A=\pi r^2[/tex]
[tex]A=\pi\times 7^2=153.86\ cm^2[/tex]
Thus the area for the vase will be [tex]A=153.86\ cm^2[/tex] ar radius r= 7 cm
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Jayce and Lara each made q bowl of punch. Lara used 6 times as much as much lemonade as Jayce did. if Jayce used 3/4 if a cup of lemonade, how many cups did Lara use?
Answers
Answer: 4.5
Step-by-step explanation:
6 x 3/4 = 18/4 divided that and it equals 4.5
I DONT KNOW WHAT IS 89090x908
Answers
Answer:
80 893 720
Step-by-step explanation:
hope dis helps!!!!